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Proof step 9 from proof int2int-neg (previous step)

n→i(# int2bits(~ j)) = i + 1, 0 ≤ 2 ^ i, j + 1 < 2 ^ i, 0 < 2 ^ i + j, 2 ^ (i + 1) + j < 0, j < 0, 2 ^ (i + 1) + 1 < 2 ^ i, 2 ^ (i + 1) + j < 2 ^ i, (2 ^ (i + 1) + j) + 1 < 2 ^ i, 2 ^ (i + 1) < 2 ^ i, j < 2 ^ i, 1 < 2 ^ i, 0 < 2 ^ i ⊦ j = bits2int(int2bits(2 ^ (i + 1) + j).rest)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j

Rule argument

seq: ⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j subst: [i, j] → [i, 2] rotate: F spec: int-pot inst: name: succ

Additional information

Used simplifier rules: ⊦ 0 < i → (0 < i ^ j ↔ i = 1 ∨ 0 ≤ j);% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ 0 ≤ j1 ∧ j1 < j → (i0 * j + j1 < j ↔ i0 ≤ 0);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i; Used terms: i, 2